The classical Nernstian description of the response of a glass electrode is given by Equation (1)
E = E0 + s log[H+] (1)
which gives the measured electrode potential, E, as a function of the proton (hydronium ion) concentration, [H+]. There are two constants in the equation, E0 and s. The first, E0, the "standard potential"; or "cell constant", gives the net electrical potential generated between the test solution and the reference cell. It is a function of the particular reference cell (usually Ag/Ag+ and located within the electrode), of the type of glass used for the electrode and of the junction potential formed at the interface between the test and reference solutions. The second constant, s, is the standard Nernstian slope parameter, ideally equal to RT/F (= T/5.04 mV or 59.128 mV at 298 K).
Normally the "cell constant", E0, is just that, a constant. However it may vary if there is a significant change in the composition of the test solution since this variation changes the "junction potential". This electrochemical potential is a well known phenomenon, theoretical treatments have been given long since (Henderson 1907, 1908). Indeed, these potentials are universally present in all potentiometric experiments which rely on an ionic bridge between solutions of differing electrolytic composition. Normally the junction potential remains constant but a correction must be applied for its variation when there is a significant change in the composition of the test solution"s electrolyte, e.g. the substitution of potassium ions, K+, for protons, H+, as may occur when titrating to very low pH.
This error may be compensated for by including an extra term in the equation for the electrode response, the junction potential correction, jp, as in Equation (2).
E = E0 + s log[H+] + jp [H+] (2)
Note that the jp coefficient has the dimensions voltage/concentration. The use of junction potential corrections has been the subject of a relatively recent review Baes, 1976). This source also gives a compilation of reported values for the correction term jp. Typical values/mV dm3 mole-1 reported when substituting H+ for any of the common alkali cations (Li+, Na+ or K+) vary between 20 and 60.
The program VLpH is designed for use in the calibration of a glass electrode in terms of hydrogen ion concentration at very low pH. The calibration process is accomplished in two stages.
Ecorr = E - jp [H+] = E0 + s log[H+] (3)
and export the adjusted data, to Hyperquad, for example.
"CO2 free" water may be used for the preparation of solutions (made by boiling distilled or de-ionised water and cooling under an inert gas), although this is hardly necessary for highly acidic solutions.
The simplest and most reliable method to calibrate the electrode is to dilute an acid stock (e.g. HCl, precisely standardized) into the test solution (e.g. KCl). This procedure has the advantage that it requires only one standardized solution, the acid. The best results will be obtained if the ionic strength is matched between the two solutions (e.g. use 0.1 M HCl and KCl). Incremental additions of acid should be selected so as to give at least 10 additions between pH 3.5 and 2.5 (where junction potential corrections are insignificant) and at least another 10 points by the end of the calibration. Choose the volumes of the additions so as to give an approximately linear variation in pH. Additions of acid may be made up to half the volume of electrolyte initially taken (e.g. a 50 mL solution of KCl may be titrated with up to 25 mL of HCl), greater additions tend to give poor results and are of little value since they give insignificant changes on the logarithmic pH-scale.
The concentration selected for the acid and electrolyte will affect the final pH, e.g. use of 0.1 M HCl/KCl limits the calibration to pH > 1.5, increasing the concentrations to 1 M limits the calibration to pH > 0.5
Use of a "titration" strategy , i.e. neutralization of an acid solution (e.g. HCl) with base (e.g. KOH) is not recommended since there are large variations in ionic strength when titrating such a highly acidic solution.
Select an electrode in which the liquid-liquid junction is in good condition, i.e. freely flowing and not fouled by precipitates, also ensure that the electrode filling solution is topped up. Place the electrode so that the level of the filling solution is well above the final level of the calibration solution - if the filling solution is below the level of the calibration solution then this will reverse the flow across the liquid-liquid junction and give rise to spurious potentials.
C.F. Baes and R.E. Mesmer, The Hydrolysis of Cations, 1976. Wiley, New York.
Henderson, Z. Phys. Chem., 59 (1907) 118.
Henderson, Z. Phys. Chem., 63 (1908) 325.
Contents > Experimental: Errors | Potentiometry > Electrode calibration | Very low pH calibration